Question 1

Given the function $$f(x) = x^3$ - 3x^2$ - 9x + 5$$, determine the intervals on which the function is increasing.

Accepted Answer

$$(-\infty, 0) \cup (3, \infty)$$

Question 2

A farmer has 200 ft of fencing to enclose a rectangular area. If the enclosed area is $$A$$ and the length is $$x$$, express $$A as a $$function of $$x.$$

Accepted Answer

$$A(x) = x(100 - x)$$

Question 3

Which of the following is the correct graph for the system of equations $$\begin{cases} y = 2x - 1 \ y = -x + 2 \end{cases}$$?

Accepted Answer

Graph A: Lines intersect at $$(1, 1)$$

Question 4

For the function $$f(x) = x^2$ - 3x + 2$$, construct and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$2x - 3 + h$$

Question 5

Given $$f(x) = \sqrt{x - 1}$$, find the domain of $$f.$$

Accepted Answer

$$x \geq 1$$

Question 6

Find all $$x$$ such that $$f(x) = 0$$ for $$f(x) = x^2$ - 4x + 3.$$

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 7

Suppose the point $$P is $$symmetric to the point $$(2, 3)$$ with respect to the $$y-$$axis. What are the coordinates of $$P$$?

Accepted Answer

$$(-2, 3)$$

Question 8

Which of the following equations represents a parabola that opens downward and has vertex at $$(0, 4)$$?

Accepted Answer

$$y = -x^2$ + 4$$

Question 9

If $$f(x) = 2x^2$ - 5x + 3$$, what is $$f(4)$$?

Accepted Answer

Question 10

Given $$f(x) = x^2$ and g(x) = x + 1$, find (f$$ \circ g)(2)$$.

Accepted Answer

$$9$$

Question 11

Which of the following describes the transformation of the graph of $$y = x^2$ to y = (x$$ - $$3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 12

Which of the following is the correct interval notation for the solution to $$|x - 2| \u003c 5$$?

Accepted Answer

$$(-3, 7)$$

Question 13

If $$f(x) = \sin(x)$$, which of the following statements is true about its period?

Accepted Answer

The period is $$2\pi$$

Question 14

Which of the following is the correct equation for a line passing through $$(0, 2)$$ with slope $$-3$$?

Accepted Answer

$$y = -3x + 2$$

Question 15

Given $$f(x) = x^2$ - 4$$, which of the following describes the symmetry of the function?

Accepted Answer

Even

Question 16

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, find (f$$ \circ g)(3)$$.

Accepted Answer

$$19$$

Question 17

Which of the following is the correct solution to $$2x^2 - 8 = 0$?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 18

A sound wave travels at 340 m/s and has a frequency of 850 Hz. What is its wavelength?

Accepted Answer

$$0.4 m$$

Question 19

Which of the following is the correct equation for a function whose graph is that of $$y = x^2$ but shifted left 5 units and down 3 units?

Accepted Answer

$$y = (x + 5)^2$ - 3$$

Question 20

If $$f(x) = x^2$ and g(x) = 2x$, what is (f + g)(3$$)$$?

Accepted Answer

$$15$$

College Algebra: Functions, Graphs, and Applications Study Guide

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